Write the standard form of the equation of the circle

Solution:

Standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules.

The equation of a circle can be eaily deduced, by knowing its center coordinates and radius.

A common form to write the equation of a circle is the center-radius form. The center radius form is also known as the standard form of the equation of the circle.

The center radius form or the standard form of the circle is given as:

(x - h )² + (y - k)² = r²

Where,

• h = x- coordinate of the center of a circle
• k = y- coordinate of the center of a circle
• r is the radius of the circle.

                                 "(Circle with centre at h, k )"

Let's take an example to understand this.

Example: Find the center and radius of the circle given by the equation (x - 3)² + (y + 5)² = 25.

Solution: As we see in the equation above, the center is the opposite sign of the numbers in the equation. In our equation we have x − 3 and y + 5 so our center coordinates will be (3, -5).

The square of the radius is given in the equation so to find the radius we take the square root of that number.

So, √25 = 5 = r.

Hence, the radius is 5 units.

Hence, the standard form of equation of the circle is (x - h )² + (y - k)² = r²

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Write the standard form of the equation of the circle

Summary:

The standard form of the equation of the circle is (x - h )² + (y - k)² = r²